What you'll learn
This revision guide covers everything you need to know about gravity and weight for AQA GCSE Physics. You'll understand the difference between mass and weight, learn how to calculate weight using gravitational field strength, and explore how gravity varies on different planets and celestial bodies. These concepts form essential foundations for mechanics and space physics topics.
Key terms and definitions
Mass — the amount of matter in an object, measured in kilograms (kg); mass remains constant regardless of location
Weight — the force acting on an object due to gravity, measured in newtons (N); weight varies depending on gravitational field strength
Gravitational field strength (g) — the force per unit mass experienced by an object in a gravitational field, measured in newtons per kilogram (N/kg) or metres per second squared (m/s²)
Gravitational force — the attractive force between any two masses; it acts at a distance without physical contact (a non-contact force)
Centre of mass — the point at which the entire weight of an object appears to act
Newton — the SI unit of force; one newton is the force needed to give a 1 kg mass an acceleration of 1 m/s²
Core concepts
Mass versus weight
Mass and weight are fundamentally different physical quantities that students frequently confuse. Understanding this distinction is essential for GCSE Physics.
Mass is a scalar quantity representing the amount of matter in an object. It is measured using a balance or electronic scales and expressed in kilograms. Your mass remains 70 kg whether you're in London, Kingston, or on the Moon.
Weight is a vector force that results from the gravitational attraction between an object and a massive body (typically Earth). It is measured using a newtonmeter (spring balance) and expressed in newtons. Your weight changes depending on where you are in the universe because gravitational field strength varies.
Key differences:
- Mass is measured in kg; weight is measured in N
- Mass is a scalar; weight is a vector (acts downward toward the centre of the gravitational field)
- Mass is constant; weight varies with location
- Mass is measured with a balance; weight is measured with a newtonmeter
The weight equation
The relationship between weight, mass, and gravitational field strength is expressed by this equation (given on your equation sheet):
W = mg
Where:
- W = weight in newtons (N)
- m = mass in kilograms (kg)
- g = gravitational field strength in N/kg or m/s²
On Earth's surface, g ≈ 9.8 N/kg (often approximated to 10 N/kg for simpler calculations). This means every kilogram of mass experiences a gravitational force of approximately 10 newtons.
The equation can be rearranged using the triangle method:
- W = mg (to find weight)
- m = W/g (to find mass)
- g = W/m (to find gravitational field strength)
Gravitational field strength on Earth
Earth's gravitational field strength at the surface is approximately 9.8 N/kg. For most GCSE calculations, you may use g = 10 N/kg unless the question specifies otherwise or requires greater precision.
The value of g decreases with altitude (height above Earth's surface) because you move further from Earth's centre of mass. However, this decrease is negligible for typical heights—climbing a mountain or flying in an aircraft produces minimal change in your weight.
Gravitational field strength also varies slightly with latitude due to Earth's rotation and its slightly oblate shape (wider at the equator than the poles). These variations are small and typically ignored at GCSE level.
The units N/kg and m/s² are equivalent:
- N/kg emphasizes the force per unit mass
- m/s² emphasizes the acceleration that gravity produces (as per Newton's second law, F = ma)
Weight as a force
Weight always acts vertically downward toward the centre of the gravitational field (toward Earth's centre). As a force, weight can:
- Cause objects to accelerate downward when dropped (free fall)
- Be balanced by other forces (such as normal contact forces when an object rests on a surface)
- Do work when objects fall through a distance
- Create tension in supports or compression in foundations
When an object rests on a surface, its weight acts downward while the surface provides an equal and opposite reaction force (normal contact force) acting upward. These forces are balanced, so the object remains stationary.
When suspended from a string or cable, an object's weight creates tension in the support equal to the weight (assuming the system is in equilibrium).
Gravity on other planets and celestial bodies
Gravitational field strength varies throughout the universe depending on the mass and radius of the celestial body. Larger masses create stronger gravitational fields, but the effect diminishes with distance from the centre.
Approximate gravitational field strengths:
| Celestial body | g (N/kg) | Relative to Earth |
|---|---|---|
| Mercury | 3.7 | 0.38× |
| Venus | 8.9 | 0.91× |
| Earth | 9.8 | 1.00× |
| Moon | 1.6 | 0.16× |
| Mars | 3.7 | 0.38× |
| Jupiter | 25 | 2.5× |
| Saturn | 11 | 1.1× |
| Sun | 274 | 28× |
An astronaut with a mass of 80 kg would have:
- Weight on Earth: W = 80 × 9.8 = 784 N
- Weight on Moon: W = 80 × 1.6 = 128 N
- Weight on Jupiter: W = 80 × 25 = 2000 N
The astronaut's mass remains 80 kg in all locations, but their weight changes dramatically.
Measuring weight and mass
Different instruments measure mass and weight:
Measuring mass:
- Top-pan balance — compares the object's mass with known masses
- Electronic balance — uses strain gauges to determine mass
- These instruments give the same reading regardless of gravitational field strength
Measuring weight:
- Newtonmeter (spring balance) — uses Hooke's law; extension of a spring is proportional to the applied force
- Calibrated spring scales — similar principle but calibrated to show weight in newtons
- These instruments would give different readings on different planets
A crucial point: bathroom scales typically show mass in kg, but they actually measure the force (weight) you exert on them, then calculate mass by assuming g = 9.8 N/kg. The same scales would give an incorrect reading on the Moon unless recalibrated.
Worked examples
Example 1: Calculating weight on Earth
Question: A student has a mass of 55 kg. Calculate her weight on Earth. (g = 9.8 N/kg)
Solution:
Given information:
- m = 55 kg
- g = 9.8 N/kg
- W = ?
Using the equation: W = mg
W = 55 × 9.8
W = 539 N
Answer: The student's weight is 539 N (accept 540 N for 2 significant figures)
Mark scheme notes: 1 mark for correct substitution into W = mg; 1 mark for correct answer with unit
Example 2: Comparing weight on different planets
Question: An object has a weight of 600 N on Earth where g = 10 N/kg.
(a) Calculate the mass of the object. [2 marks]
(b) Calculate the weight of the same object on Mars where g = 3.7 N/kg. [2 marks]
(c) Explain why the weight is different on Mars but the mass is the same. [2 marks]
Solution:
(a) Given: W = 600 N, g = 10 N/kg
Rearranging W = mg to find mass: m = W/g
m = 600/10
m = 60 kg
Answer: The mass is 60 kg
(b) Given: m = 60 kg, g = 3.7 N/kg
Using W = mg:
W = 60 × 3.7
W = 222 N
Answer: The weight on Mars is 222 N
(c) Explanation: Weight is the force due to gravity acting on the object's mass. Mars has a weaker gravitational field strength than Earth (3.7 N/kg compared to 10 N/kg), so the gravitational force (weight) is less. Mass is the amount of matter in the object, which doesn't change with location.
Mark scheme notes: (a) 1 mark for rearrangement, 1 mark for answer with unit; (b) 1 mark for substitution, 1 mark for answer with unit; (c) 1 mark for explaining weight depends on gravitational field strength, 1 mark for explaining mass is constant/amount of matter
Example 3: Finding gravitational field strength
Question: An astronaut has a mass of 85 kg. On a distant planet, she measures her weight as 323 N using a newtonmeter.
Calculate the gravitational field strength on this planet. [3 marks]
Solution:
Given information:
- m = 85 kg
- W = 323 N
- g = ?
Rearranging W = mg:
g = W/m
g = 323/85
g = 3.8 N/kg
Answer: The gravitational field strength is 3.8 N/kg
(This is similar to Mars or Mercury)
Mark scheme notes: 1 mark for selecting W = mg; 1 mark for correct rearrangement; 1 mark for correct answer with unit
Common mistakes and how to avoid them
Confusing mass and weight — Remember: mass is measured in kg and stays constant; weight is measured in N and changes with gravitational field strength. If a question asks for weight, your answer must be in newtons, not kilograms.
Forgetting units in calculations — Always include units in your final answer. Writing "539" without "N" for weight will lose you the final mark. Similarly, mass needs "kg" and gravitational field strength needs "N/kg".
Using the wrong value for g — Check whether the question specifies g = 9.8 N/kg or g = 10 N/kg. For Earth, use the value given in the question. For other planets, the value will always be provided in the question or data sheet.
Mixing up which instrument measures what — A balance (top-pan or electronic) measures mass in kg. A newtonmeter (spring balance) measures force/weight in N. Bathroom scales appear to show mass but actually measure weight and convert it.
Thinking mass changes in space — An astronaut's mass remains constant whether on Earth, the Moon, or in deep space. Only their weight changes because gravitational field strength varies. Even in "zero gravity" (free fall), mass is unchanged.
Not rearranging the equation correctly — Practice using the formula triangle or algebraic rearrangement. Common errors include calculating g = m/W instead of g = W/m. Always write out what you're finding and check your rearrangement makes sense (e.g., if mass increases and g stays constant, weight must increase).
Exam technique for "Gravity and weight"
Command word awareness — "Calculate" requires you to show working and give a numerical answer with units (typically 2-3 marks). "State the difference between" needs clear distinct points for mass vs weight (typically 1 mark per difference, up to 2 marks). "Explain" requires reasoning, not just stating facts.
Show all working — Even if you get the final answer wrong, you can earn method marks for correct equation selection, substitution, and rearrangement. Write W = mg, then substitute values, then calculate. Never just write a final number.
Significant figures and rounding — Unless specified otherwise, give answers to 2 or 3 significant figures. Match the precision of data given in the question. For g = 10 N/kg calculations, 2 significant figures is usually appropriate.
Extended response questions — When explaining why weight differs between planets but mass doesn't (a common 4-6 mark question), use a clear structure: define mass, define weight, explain the role of gravitational field strength, give an example with values if possible. Use correct scientific terminology throughout.
Quick revision summary
Mass is the amount of matter in kg; weight is the gravitational force in N. Weight equals mass times gravitational field strength: W = mg. On Earth, g ≈ 9.8 N/kg (or 10 N/kg for simpler calculations). Mass stays constant everywhere, but weight varies because gravitational field strength differs between planets. Measure mass with a balance (kg) and weight with a newtonmeter (N). Weight always acts downward toward the centre of the gravitational field.